# Causal Discovery from Subsampled Time Series with Proxy Variables

arXiv: https://arxiv.org/abs/2305.05276 · HTML: https://mlsanity.com/paper/2305.05276/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 61 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 7 of 7)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Causal Discovery from Subsampled Time Series Data by Constraint Optimization](https://mlsanity.com/paper/1602.07970/) (2016)
- [Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series](https://mlsanity.com/paper/1704.02519/) (2017)
- [Which Invariance Should We Transfer? A Causal Minimax Learning Approach](https://mlsanity.com/paper/2107.01876/) (2021)

## Built on by (most cited first, 8 of 8)

- [GCAD: Anomaly Detection in Multivariate Time Series from the Perspective of Granger Causality](https://mlsanity.com/paper/2501.13493/) (2025)
- [Deep Learning for Time Series Forecasting: A Survey](https://mlsanity.com/paper/2503.10198/) (2025)
- [Causal Inference with Latent Variables: Recent Advances and Future Prospectives](https://mlsanity.com/paper/2406.13966/) (2024)
- [Causal Discovery for Irregularly Time Series with Consistency Guarantees](https://mlsanity.com/paper/2507.03310/) (2025)
- [The Blessings of Multiple Treatments and Outcomes in Treatment Effect Estimation](https://mlsanity.com/paper/2309.17283/) (2023)
- [Beyond All-to-All: Causal-Aligned Transformer with Dynamic Structure Learning for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.16308/) (2025)
- [Causal Discovery from Time-Series Data with Short-Term Invariance-Based Convolutional Neural Networks](https://mlsanity.com/paper/2408.08023/) (2024)
- [ITSY: Causal Discovery From Irregular Time-Series Data](https://mlsanity.com/paper/2609.23516/) (2026)

## Abstract (arXiv)

Inferring causal structures from time series data is the central interest of many scientific inquiries. A major barrier to such inference is the problem of subsampling, i.e., the frequency of measurement is much lower than that of causal influence. To overcome this problem, numerous methods have been proposed, yet either was limited to the linear case or failed to achieve identifiability. In this paper, we propose a constraint-based algorithm that can identify the entire causal structure from subsampled time series, without any parametric constraint. Our observation is that the challenge of subsampling arises mainly from hidden variables at the unobserved time steps. Meanwhile, every hidden variable has an observed proxy, which is essentially itself at some observable time in the future, benefiting from the temporal structure. Based on these, we can leverage the proxies to remove the bias induced by the hidden variables and hence achieve identifiability. Following this intuition, we propose a proxy-based causal discovery algorithm. Our algorithm is nonparametric and can achieve full causal identification. Theoretical advantages are reflected in synthetic and real-world experiments.